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2.3 Detailed conclusion table specific for Rubi results

The following table is specific to Rubi only. It gives additional statistics for each integral. the column steps is the number of steps used by Rubi to obtain the antiderivative. The rules column is the number of unique rules used. The integrand size column is the leaf size of the integrand. Finally the ratio \(\frac {\text {number of rules}}{\text {integrand size}}\) is also given. The larger this ratio is, the harder the integral is to solve. In this test file, problem number [74] had the largest ratio of [1.83332999999999990]

# grade
number of
steps
used
number of
unique
rules
normalized
antiderivative
leaf size
integrand
leaf size
\(\frac {\text {number of rules}}{\text {integrand leaf size}}\)
1 A 6 5 1.00 12 0.417
2 A 7 6 0.98 14 0.429
3 A 8 7 0.99 14 0.500
4 A 6 6 1.15 16 0.375
5 A 4 4 1.19 16 0.250
6 A 4 4 1.09 14 0.286
7 A 1 1 1.00 8 0.125
8 A 6 5 1.00 16 0.312
9 A 4 3 1.00 16 0.188
10 A 5 4 1.01 16 0.250
11 A 7 6 1.09 16 0.375
12 A 3 3 1.05 18 0.167
13 A 3 3 1.10 18 0.167
14 A 3 3 1.16 16 0.188
15 A 3 3 1.09 10 0.300
16 A 7 6 0.98 18 0.333
17 A 11 10 0.91 18 0.556
18 A 15 14 0.95 18 0.778
19 A 4 3 0.96 18 0.167
20 A 4 3 0.95 18 0.167
21 A 4 3 0.95 16 0.188
22 A 9 8 0.91 10 0.800
23 N/A 1 0 1.00 18 0.000
24 N/A 1 0 1.00 18 0.000
25 A 2 2 1.00 18 0.111
26 A 2 2 1.00 16 0.125
27 C 12 11 1.05 10 1.100
28 N/A 1 0 1.00 18 0.000
29 N/A 1 0 1.00 18 0.000
30 N/A 2 0 1.00 18 0.000
31 A 4 3 1.00 16 0.188
32 N/A 1 0 1.00 18 0.000
33 N/A 1 0 1.00 18 0.000
34 A 3 3 0.57 30 0.100
35 A 3 3 0.60 30 0.100
36 A 3 3 0.60 28 0.107
37 A 7 7 0.69 30 0.233
38 A 7 7 0.73 30 0.233
39 A 3 3 0.53 30 0.100
40 A 3 3 0.55 30 0.100
41 A 3 3 0.53 28 0.107
42 A 3 3 0.65 30 0.100
43 A 3 3 0.50 30 0.100
44 A 3 3 0.52 30 0.100
45 A 3 3 0.50 28 0.107
46 A 3 3 0.62 30 0.100
47 A 3 3 0.60 30 0.100
48 A 3 3 0.61 30 0.100
49 A 3 3 0.70 28 0.107
50 A 1 1 1.00 23 0.043
51 A 10 9 0.73 30 0.300
52 A 14 13 0.74 30 0.433
53 N/A 1 0 1.00 34 0.000
54 A 9 8 0.97 34 0.235
55 A 8 7 0.99 32 0.219
56 A 8 7 0.99 24 0.292
57 N/A 1 0 1.00 34 0.000
58 A 10 9 1.21 10 0.900
59 A 8 7 1.30 10 0.700
60 A 9 8 1.08 8 1.000
61 A 4 3 0.94 6 0.500
62 A 9 8 1.00 10 0.800
63 A 6 5 1.07 10 0.500
64 A 8 7 1.08 10 0.700
65 A 9 8 1.15 10 0.800
66 A 11 10 1.20 10 1.000
67 A 7 6 0.92 12 0.500
68 A 6 5 0.97 12 0.417
69 A 7 6 0.95 10 0.600
70 A 5 4 1.09 8 0.500
71 A 10 9 1.01 12 0.750
72 A 12 11 0.98 12 0.917
73 A 17 16 1.01 12 1.333
74 A 23 22 1.46 12 1.833
75 A 8 7 0.89 12 0.583
76 A 9 8 0.94 10 0.800
77 A 6 5 0.95 8 0.625
78 A 11 10 1.04 12 0.833
79 A 13 12 0.92 12 1.000
80 A 20 19 0.87 12 1.583
81 A 6 5 0.87 12 0.417
82 A 7 6 0.93 10 0.600
83 A 5 4 1.00 8 0.500
84 N/A 5 0 1.00 12 0.000
85 A 5 4 0.89 12 0.333
86 A 6 5 0.92 10 0.500
87 A 7 6 0.92 8 0.750
88 N/A 5 0 1.00 12 0.000
89 A 5 4 0.88 12 0.333
90 A 6 5 0.89 10 0.500
91 A 7 6 0.90 8 0.750
92 N/A 5 0 1.00 12 0.000
93 N/A 3 0 1.00 16 0.000
94 A 6 5 0.96 16 0.312
95 A 7 6 0.98 14 0.429
96 A 7 6 1.02 12 0.500
97 N/A 5 0 1.00 16 0.000
98 A 8 7 1.06 18 0.389
99 A 9 8 1.10 16 0.500
100 C 11 10 1.05 14 0.714
101 A 9 8 1.14 16 0.500
102 A 11 10 0.99 14 0.714
103 A 9 8 1.18 16 0.500
104 C 13 12 1.01 14 0.857
105 A 8 7 0.96 18 0.389
106 A 9 8 0.98 16 0.500
107 A 9 8 1.01 14 0.571
108 A 6 5 0.96 16 0.312
109 C 11 10 1.10 14 0.714
110 A 6 5 0.94 16 0.312
111 A 11 10 1.03 14 0.714
112 A 6 5 0.94 16 0.312
113 C 13 12 1.08 14 0.857
114 A 4 3 0.98 21 0.143
115 A 7 6 0.84 21 0.286
116 A 7 6 0.91 21 0.286
117 A 7 6 0.88 21 0.286
118 A 6 5 0.96 19 0.263
119 A 1 1 1.00 10 0.100
120 C 11 10 1.25 21 0.476
121 A 7 6 0.90 21 0.286
122 A 5 4 0.92 21 0.190
123 A 8 7 0.85 21 0.333
124 A 6 5 0.92 21 0.238
125 A 9 8 0.87 21 0.381
126 A 4 3 0.96 23 0.130
127 A 10 9 0.87 23 0.391
128 A 9 8 0.88 23 0.348
129 A 8 7 0.88 23 0.304
130 A 7 6 0.93 21 0.286
131 A 5 4 1.04 12 0.333
132 C 12 11 1.33 23 0.478
133 C 10 9 0.88 23 0.391
134 A 6 5 0.87 23 0.217
135 C 12 11 0.85 23 0.478
136 N/A 4 0 1.00 23 0.000
137 A 16 15 1.02 23 0.652
138 A 14 13 1.03 23 0.565
139 A 11 10 0.91 23 0.435
140 A 9 8 0.94 21 0.381
141 A 5 4 0.93 12 0.333
142 C 13 12 1.36 23 0.522
143 C 11 10 0.86 23 0.435
144 C 13 12 1.04 23 0.522
145 C 16 15 0.85 23 0.652
146 N/A 4 0 1.00 23 0.000
147 A 13 12 1.07 23 0.522
148 A 14 13 0.99 23 0.565
149 A 10 9 0.93 21 0.429
150 A 7 6 0.97 12 0.500
151 C 14 13 1.42 23 0.565
152 C 12 11 0.85 23 0.478
153 C 14 13 1.15 23 0.565
154 C 16 15 0.86 23 0.652
155 N/A 3 0 1.00 23 0.000
156 A 6 5 0.79 23 0.217
157 A 7 6 0.82 23 0.261
158 A 6 5 0.82 23 0.217
159 C 15 14 0.99 21 0.667
160 A 10 9 0.91 12 0.750
161 N/A 4 0 1.00 23 0.000
162 A 5 4 0.81 23 0.174
163 A 5 4 0.84 23 0.174
164 A 5 4 0.84 23 0.174
165 A 11 10 0.92 21 0.476
166 C 13 12 1.02 12 1.000
167 N/A 4 0 1.00 23 0.000
168 A 8 7 1.20 23 0.304
169 C 18 17 1.15 23 0.739
170 A 16 15 1.08 23 0.652
171 C 18 17 0.98 21 0.810
172 A 12 11 0.94 12 0.917
173 N/A 4 0 1.00 23 0.000
174 A 7 6 1.16 23 0.261
175 A 14 13 1.06 23 0.565
176 C 18 17 1.09 23 0.739
177 A 14 13 0.93 21 0.619
178 C 15 14 1.03 12 1.167
179 N/A 4 0 1.00 23 0.000
180 C 10 9 0.96 25 0.360
181 A 8 7 0.91 25 0.280
182 C 10 9 0.97 25 0.360
183 A 9 8 0.94 23 0.348
184 C 11 10 1.05 14 0.714
185 N/A 4 0 1.00 25 0.000
186 A 20 19 1.22 25 0.760
187 C 21 20 1.25 25 0.800
188 A 16 15 1.20 25 0.600
189 C 16 15 1.02 23 0.652
190 A 11 10 0.99 14 0.714
191 N/A 4 0 1.00 25 0.000
192 C 20 19 1.22 25 0.760
193 A 14 13 1.18 25 0.520
194 C 18 17 1.19 25 0.680
195 A 12 11 0.95 23 0.478
196 C 13 12 1.01 14 0.857
197 N/A 4 0 1.00 25 0.000
198 F 0 0 N/A 0.000 N/A
199 C 25 24 1.46 25 0.960
200 A 28 27 1.36 25 1.080
201 C 19 18 0.99 23 0.783
202 A 13 12 0.97 14 0.857
203 N/A 4 0 1.00 25 0.000
204 A 6 5 0.92 25 0.200
205 A 7 6 0.94 25 0.240
206 A 6 5 0.93 25 0.200
207 C 13 12 1.08 23 0.522
208 A 9 8 1.01 14 0.571
209 N/A 4 0 1.00 25 0.000
210 A 5 4 0.92 25 0.160
211 A 5 4 0.94 25 0.160
212 A 5 4 0.93 25 0.160
213 A 10 9 1.03 23 0.391
214 C 11 10 1.10 14 0.714
215 N/A 4 0 1.00 25 0.000
216 A 8 7 1.39 25 0.280
217 C 16 15 1.32 25 0.600
218 A 15 14 1.24 25 0.560
219 C 16 15 1.03 23 0.652
220 A 11 10 1.03 14 0.714
221 N/A 4 0 1.00 25 0.000
222 A 7 6 1.31 25 0.240
223 A 13 12 1.24 25 0.480
224 C 16 15 1.20 25 0.600
225 A 13 12 1.02 23 0.522
226 C 13 12 1.08 14 0.857
227 N/A 4 0 1.00 25 0.000
228 A 10 9 1.08 23 0.391
229 A 7 6 1.10 23 0.261
230 A 9 8 1.10 23 0.348
231 A 6 5 1.11 23 0.217
232 A 8 7 1.11 23 0.304
233 A 5 4 1.09 23 0.174
234 A 9 8 1.08 23 0.348
235 A 6 5 1.10 23 0.217
236 A 4 3 1.01 25 0.120
237 A 4 3 1.01 25 0.120
238 A 4 3 1.01 25 0.120
239 A 4 3 1.01 25 0.120
240 A 4 3 0.99 25 0.120
241 A 4 3 0.99 25 0.120
242 A 4 3 0.98 25 0.120
243 A 4 3 1.01 25 0.120
244 N/A 4 0 1.00 25 0.000
245 N/A 4 0 1.00 25 0.000
246 N/A 4 0 1.00 25 0.000
247 N/A 4 0 1.00 25 0.000
248 N/A 4 0 1.00 25 0.000
249 N/A 4 0 1.00 25 0.000
250 N/A 4 0 1.00 25 0.000
251 N/A 4 0 1.00 25 0.000
252 N/A 4 0 1.00 25 0.000
253 N/A 4 0 1.00 25 0.000
254 N/A 4 0 1.00 25 0.000
255 N/A 4 0 1.00 25 0.000
256 N/A 4 0 1.00 25 0.000
257 N/A 4 0 1.00 25 0.000
258 N/A 4 0 1.00 25 0.000
259 N/A 4 0 1.00 25 0.000
260 A 8 7 0.93 30 0.233
261 A 7 6 0.94 30 0.200
262 A 5 4 0.92 28 0.143
263 A 6 5 0.94 30 0.167
264 A 9 8 0.92 30 0.267
265 A 6 5 0.89 30 0.167
266 A 16 15 1.28 30 0.500
267 A 12 11 1.20 30 0.367
268 A 8 7 1.09 28 0.250
269 A 6 5 0.89 30 0.167
270 A 6 5 1.02 30 0.167
271 A 11 10 1.31 30 0.333
272 A 3 2 1.00 30 0.067
273 A 3 2 1.00 30 0.067
274 A 3 2 1.00 28 0.071
275 A 3 2 1.00 30 0.067
276 A 3 2 1.00 30 0.067
277 A 3 2 1.00 30 0.067
278 C 11 10 1.03 30 0.333
279 C 10 9 1.08 30 0.300
280 A 4 3 0.96 28 0.107
281 N/A 3 0 1.00 30 0.000
282 N/A 4 0 1.00 30 0.000
283 A 6 5 1.12 10 0.500
284 A 4 4 1.06 10 0.400
285 A 4 3 0.97 8 0.375
286 A 5 5 1.07 6 0.833
287 C 9 8 1.24 10 0.800
288 A 3 3 1.00 10 0.300
289 A 6 5 1.00 10 0.500
290 A 6 6 1.03 10 0.600
291 C 9 8 1.24 10 0.800
292 A 8 7 1.14 10 0.700
293 A 7 6 1.09 8 0.750
294 A 7 6 0.97 6 1.000
295 C 9 8 1.41 10 0.800
296 A 3 3 1.00 10 0.300
297 A 4 4 1.11 10 0.400
298 A 5 5 1.16 10 0.500
299 A 6 6 1.19 10 0.600
300 A 7 6 1.00 10 0.600
301 A 3 3 1.00 8 0.375
302 A 6 5 1.00 6 0.833
303 C 9 8 1.25 10 0.800
304 A 3 3 1.00 10 0.300
305 A 6 5 1.12 10 0.500
306 A 6 5 1.07 10 0.500
307 A 3 3 1.00 10 0.300
308 A 3 3 1.00 10 0.300
309 A 3 3 1.00 8 0.375
310 A 3 3 1.00 6 0.500
311 C 9 8 1.13 10 0.800
312 A 3 3 1.00 10 0.300
313 A 3 3 1.01 10 0.300
314 A 3 3 1.00 20 0.150
315 A 2 2 0.98 20 0.100
316 A 2 2 1.00 20 0.100
317 A 1 1 1.00 18 0.056
318 A 1 1 1.00 20 0.050
319 A 1 1 1.00 20 0.050
320 A 2 2 1.03 20 0.100
321 A 3 3 1.00 20 0.150
322 A 2 2 0.98 20 0.100
323 A 2 2 1.00 20 0.100
324 A 1 1 1.00 18 0.056
325 A 1 1 1.00 20 0.050
326 A 1 1 1.00 20 0.050
327 A 2 2 1.03 20 0.100
328 A 2 2 0.99 22 0.091
329 A 2 2 1.00 22 0.091
330 A 1 1 1.00 22 0.045
331 A 1 1 1.00 22 0.045
332 A 1 1 1.00 22 0.045
333 A 2 2 0.99 22 0.091
334 A 2 2 0.99 22 0.091
335 A 2 2 0.99 22 0.091
336 A 2 2 1.01 22 0.091
337 A 1 1 1.00 22 0.045
338 A 1 1 1.00 22 0.045
339 A 1 1 1.00 22 0.045
340 A 2 2 0.99 22 0.091
341 A 2 2 0.99 22 0.091
342 N/A 1 0 1.00 40 0.000
343 C 12 11 1.12 40 0.275
344 C 11 10 1.12 40 0.250
345 C 10 9 1.08 38 0.237
346 N/A 1 0 1.00 40 0.000
347 N/A 1 0 1.00 40 0.000
348 C 10 9 1.08 10 0.900
349 A 7 6 0.87 12 0.500
350 A 6 5 0.90 12 0.417
351 A 7 6 0.87 10 0.600
352 A 6 5 1.00 8 0.625
353 A 3 3 1.00 12 0.250
354 A 3 3 1.00 12 0.250
355 A 3 3 1.00 12 0.250
356 A 3 3 1.00 12 0.250
357 A 3 3 1.00 12 0.250
358 A 7 6 0.91 14 0.429
359 A 6 5 0.92 14 0.357
360 A 7 6 0.94 12 0.500
361 A 4 3 0.97 10 0.300
362 N/A 1 0 1.00 14 0.000
363 N/A 1 0 1.00 14 0.000
364 C 11 10 1.13 19 0.526
365 A 5 4 1.00 15 0.267
366 A 5 4 0.78 12 0.333
367 A 5 4 0.80 14 0.286
368 A 7 6 1.00 10 0.600
369 F 0 0 N/A 0.000 N/A
370 A 3 2 1.00 26 0.077
371 A 3 2 1.00 26 0.077

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